Unless every monster just becomes a human with a different form, unless you get rid of a core concept of D&D having monsters that are monsters, I think there will always be issues. Without alignment people will point to the picture and the description and saying how dare you make a monster out of [insert group or ethnicity here].The main complaint is about the humanoid race.
They can create a section : humanoids society
Evil cult driven, with the Drow as sample.
Militaristic society, Hobgoblin as sample.
Pillager society, Orc as sample.
Each humanoid race in the MM can be presented as a Sample of polarized society. With a warning that you can use any race or create a new one for those sample.
That will give a sanitized MM.
Much like the "alignment horror stories" that are really about bad DMs and jerk players unless you get rid of monsters, removing alignment doesn't do anything other than take away a core representation of how the average monster of that type tends to interact with the world.